Question

How do I find an interest rate using the formula `a=p(1+r)^t`?

Answer 1

To find the interest rate (r) in the formula `a=p(1+r)^t`, you need to know the values of a (amount), p (principal) and t (time). You would take a and divide it by p. You will then take that result and take the t root of it. You then subtract that answer by 1 to get your interest rate in decimal form.

Here is an example:

You need to find the interest rate of an account that grew from $4000 to $4063 in 2 years.

`a = 4063`

`p = 4000`

`t = 2`

`4063 = 4000 (1 + r)^2`

`4063/4000=(1 +r)^2`

`1.01575 = (1 +r)^2`

`sqrt1.01575=sqrt((1 +r)^2)`

`1.007844 = 1 + r`

`1.007844 - 1 = r`

`.007844 = r`

interest rate rounds to `.784 %`